推 Elfiend:原式改寫成(x-π/4)/cot2x再羅必達的算式很簡短220.139.177.197 04/21
※ 引述《anson0810 (奇  )》之銘言：
: lim
: x->pi/4 (x-pi/4)tan2x
: 請問一下這一題的答案是0嗎?
令y=x-pi/4
lim
則原式= y->0 y*tan(2y+pi/2)
lim
= y->0 y*{-cot(2y)}
lim
= y->0 -cot(2y)/(1/y)
lim
= y->0 2(csc2y)^2/(-1/y^2)
lim
= y->0 (-2)*{y^2/(six2y)^2}
lim
= y->0 (-2)*(1/4)(2y/six2y)^2
= (-1/2)(1)^2=-1/2
#
參考看看囉~~
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